Question is why do we take theta value of pie/2 and not pie/6. i have done other questions as well. some time we take theta value which we get thrrough sin and some times the one we get through coz.WHY IS THAT ...PLZ HELP

For your first question, the wording is a little strange and confusing but what I think they're talking about is that only the part that's left over after a multiple of is significant. For example, if you had something like , well that's just the same as because after you take out you have just 1 left.

For the second part, I'm confused as to how you got . It should be because

so, and

You take the value of theta that works for BOTH equations, in this case